package lc.动态规划;

/**
 * @description: 最小路径和
 * @author: qian
 * @createDate: 2021/9/14
 */
public class Math64 {

    public int minPathSum(int[][] grid) {

        int r = grid.length; // 行

        int c = grid[0].length; // 列

        int [][]dp = new int[r][c];

        dp[0][0] = grid[0][0];// 0-0的最短路径存在dp[0][0]

        for (int i = 1; i < c; i++) { // 计算i 列的最短路径
            dp[0][i] = dp[0][i - 1] + grid[0][i];
        }
        for (int i = 1; i < r; i++) { //计算i 行的最短路径
            dp[i][0] = dp[i - 1][0] + grid[i][0];
        }

        for (int i = 1; i < r; i++) {
            for (int j = 1; j < c; j++) {
                // 上面和左边最小值加上原位置
                dp[i][j] = Math.min(dp[i - 1][j],dp[i][j - 1]) + grid[i][j];
            }
        }
        return dp[r - 1][c - 1];
    }
}
